What is the significance of Captain Walton's letters in Frankestein?
Captain Walton provides the frame story in Frankenstein, the fictional epistolary method by which the entire story is composed and recorded. Walton corresponds with his sister, recounting how he discovered Victor Frankenstein on the Arctic ice, and what effect Frankenstein's story (and later the Monster's story) had on him. Writing it down also allows Walton to study and consider Frankenstein's life in detail later.
This manuscript will doubtless afford you the greatest pleasure; but to me, who know him, and who hear it from his own lips -- with what interest and sympathy shall I read it in some future day!
(Shelley, Frankenstein, gutenberg.org)
The letters give Walton a reason to be recording the story; without a secondary audience (the reader being the primary audience), Walton would have no reason to be writing Frankenstein's story down. This also shows the difference between Walton and Frankenstein; Walton has a strong relationship with his family and wishes to include them vicariously in his life, while Frankenstein has isolated and alienated himself from everyone around him.